Tens of thousands of demonstrators converged on Wisconsin’s state Capitol today in frigid weather to protest a Republican plan to curb the power of public sector unions.

The rotunda of the Capitol was choked with protesters hours before a planned union-backed rally scheduled to start at 3 p.m. local time, and a lengthy line snaked around outside a single open building entrance.

Today’s rally had a festival or concert feel with a stage set up and some popular musicians expected to perform later in the day. Madison police said they expected a “sizable crowd” but did not give an estimate.

U.S. labor groups hoped to turnout the largest crowds yet in demonstrations planned for every state capital in the nation on Saturday to show solidarity with Wisconsin in fighting the proposal they see as trying to break the union movement.

Sporadic protests were staged in several cities around the country over the last two weeks but the plans on Saturday were the most ambitious yet by organized labor.

In Illinois, where 14 Wisconsin senators fled earlier this month to prevent a vote on the union bill, organizers estimated 2,000 demonstrators turned out in downtown Chicago on Saturday to show solidarity with Wisconsin workers.

In Columbus, Ohio several hundred protesters turned out for a similar solidarity rally.

What began two weeks ago as Republicans in one relatively small U.S. state trying to balance the budget by rewriting local labor relations rules has turned into a major national confrontation.

If Republicans prevail in Wisconsin, a number of other states governed by conservative majorities could follow and deal a serious blow to union power. Already, other legislatures including Ohio, Indiana, Iowa, Idaho, Tennessee, and Kansas are working on union curbs.

The stakes are high for labor because more than a third of public employees such as teachers, police and civil service workers belong to unions while only about six percent of private sector workers are unionized. Unions are the biggest single source of funding for the Democratic party.

At least 2,500 demonstrators stood under new Republican Gov. Scott Walker’s office window by midday in a position Tea Party supporters of the governor occupied a week ago, and a thick blanket of demonstrators marched around the building.

To get there, protesters braved temperatures expected to reach only a high of 19 degrees Fahrenheit on Saturday.

Wearing thick outerwear and her 10-month-old son strapped to her belly, Tamarine Cornelius, 36, carried a sign that read “If Wisconsin is gonna become Mississippi than I am gonna want better weather.”

“I understand that there are tough times ahead, things are going to be difficult no matter what. I think most people understand that,” said Cornelius, who works for the non-profit Wisconsin Council on Children and Families.

Inside the already crowded Capitol, Dave Higginbotham, 45, a county transportation worker in southern Wisconsin near the Illinois border, said curbs on union powers could make personal connections with the boss more important than job performance.

“To work in that type of environment, if you’re someone that works hard and is concentrated on the taxpayers and what’s important to them, becomes second nature and it gets frustrating, really frustrating,” Higginbotham said.

The Saturday protests take place in a different context than previous rallies, after the controversial proposal passed the state Assembly on Friday, testing the resolve of a movement that has so far been remarkably peaceful.

Backers of the bill won a major victory early Friday with state Assembly approval of the union bill. The bill has now moved to the state Senate where it is stalled because the 14 Democrats fled to Illinois to deny a quorum for a vote.

People in the state capital of Madison, which is home to unionized state government agencies and the University of Wisconsin, are overwhelmingly opposed to the governor’s plan. But Republicans said they believe there is a silent majority who voted Walker into office, and support the efforts.

Willetta Shanklin of Oak Creek, Wisconsin, near Milwaukee, said on Thursday that she supports the governor.